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Playing from the score at first sight is sight reading, thereafter it is reading.

I agree. Sight-reading = prima vista. Practicing a piece in progress or performing a finished piece while still referring to the score is not sight-reading in the common usage of the term. Again, from The Harvard Dictionary of Music (4th ed.):

Sight-reading, sight-singing. The performing of a piece of music on seeing it for the first time. . . . Performing at sight on an instrument requires the ability to grasp the meaning of musical notation quickly and call upon the relevant technical skills for execution; this should be accompanied by the skills of the ear as well. The ability to perform efficiently at sight and the ability to give finished performances of distinction do not necessarily go together, and both should be among the goals of musical instruction.

What a good response tangleweeds and Bobpickle. I've had people say they sight read but don't really do so if they haven't seen the music before. Thanks for posting the distinction. I may have been guilty of this myself a couple or 6 times <blush>

I can't see practicing a piece with each hand separately as anything but an intensive preparation method for undertaking technically difficult (for ones level) material. In that sense it is akin to writing in fingerings, playing isolated passages or figures repeatedly until mastered or spending lesson time breaking down a piece musically with ones teacher.

Doing these sorts of things once only, at speed, on pieces of music one after another being seen for the very first time seems a complete waste of effort. It would be like going to the gym and doing one bicep curl, one pushup, one stroke on the rowing machine and so forth and calling it a workout.

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Current Life+Music Philosophy: Less Thinking, More Foot Tapping

One of the key skills in sight reading is integration (reading both staves simultaneously), and when you isolate the clefs you obviously eliminate that. In sight reading, the difficulty of reading both staves together is greater than the sum of each individually, if that makes any sense.

HS practice is a wll known practice method and it is really helpful. but why not in sight reading practice because even some advanced pianist have sight reading problem but no one suggest HS practice?

As others have mentioned, working through a piece HS is sort of at odds with the meaning and purpose of sight reading. However, good beginners sight reading material will often be written with little HT going on to keep things simple. The ABRSM takes this approach, excluding HT altogether from grade 1 sight reading. Excerpt from their syllabus about grade 1:

“a four- or six-bar piece in 4/4, 3/4 or 2/4 in C, G or F majors, A or D minors, with each hand playing separately and in a ﬁve-ﬁnger position. Simple dynamics, note values, articulations and occasional accidentals (within minor keys only) may be encountered.”